import numpy as np
import pandas as pd

from itertools import cycle
from scipy import interp
import more_itertools as mit

# sklearn
from sklearn import metrics
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler

# Tensorflow
import tensorflow as tf
tf.random.set_seed(123)

# Timer
from timeit import default_timer as timer

# Visualisation libraries

## IPython
from IPython.display import clear_output

## Text
from colorama import Fore, Back, Style
from IPython.display import Image, display, Markdown, Latex

## seaborn
import seaborn as sns
sns.set_context('paper', rc={'font.size':12,'axes.titlesize':14,'axes.labelsize':12})
sns.set_style('whitegrid')

## matplotlib
import matplotlib
import matplotlib.pyplot as plt
from matplotlib.patches import Ellipse, Polygon
import matplotlib.gridspec as gridspec
import matplotlib.colors
from pylab import rcParams
from matplotlib.font_manager import FontProperties
plt.rcParams['figure.figsize'] = 14, 8
plt.rcParams['axes.labelsize'] = 14
plt.rcParams['xtick.labelsize'] = 12
plt.rcParams['ytick.labelsize'] = 12
plt.rcParams['text.color'] = 'k'
%matplotlib inline

## plotly
from plotly.offline import init_notebook_mode, iplot 
import plotly.graph_objs as go
import plotly.offline as py
from plotly.subplots import make_subplots
import plotly.express as px
# %config InlineBackend.figure_format = 'retina' 

import warnings
warnings.filterwarnings("ignore")

Heart Disease Dataset

In this article, we demonstrate solving a classification problem in TensorFlow using Estimators using the Heart Disease Dataset from the UCI Machine Learning Repository.

Picture Source: harvard.edu

Attribute Information:

1. Age
2. Sex
   • 0: Female
   • 1: Male
3. Chest Pain Type
   • 1: Typical Angina
   • 2: Atypical Angina
   • 3: Non-Anginal Pain
   • 4: Asymptomatic

• Resting Blood Pressure

1. Serum Cholestoral (in mg/dl )
2. FBS: Fasting Blood Sugar > 120 mg/dl
   • 0 = False
   • 1 = True
3. Resting Electrocardiographic Results
   • 0: normal
   • 1: having ST-T wave abnormality (T wave inversions and/or ST elevation or depression of > 0.05 mV)
   • 2: showing probable or definite left ventricular hypertrophy by Estes' criteria
4. Maximum Heart Rate Achieved
5. Exercise Induced Angina
   • 0: No
   • 1: Yes
6. Oldpeak = St Depression Induced By Exercise Relative To Rest
7. Slope: The Slope Of The Peak Exercise ST Segment
   • 1: Upsloping
   • 2: Flat
   • 3: Downsloping
8. Number Of Major Vessels (0-3) Colored By Flourosopy
9. Thal
   • 3: Normal
   • 6: Fixed Defect
   • 7: Reversable Defect

Variable to be predicted

• Heart Disease
  • 0: Absence
  • 1: Presence

Problem Description

The object of the exercise is to develop a predictive model that can predict whether heart disease is present or absent based on the rest of the given features.

Data = np.genfromtxt('heart-disease/heart.dat', delimiter=' ')
Attributes = ['Age', 'Sex', 'Chest Pain Type', 'Resting Blood Pressure', 'Serum Cholestoral',
              'Fasting Blood Sugar', 'Resting Electrocardiographic Results', 'Maximum Heart Rate Achieved',
              'Exercise Induced Angina', 'Oldpeak', 'Slope',
              'Number of Major Vessels', 'Thal', 'Heart Disease']
Data = pd.DataFrame(data = Data, columns = Attributes)
# 
Temp = ['Sex', 'Chest Pain Type', 'Fasting Blood Sugar', 'Resting Electrocardiographic Results',
       'Exercise Induced Angina', 'Slope', 'Number of Major Vessels','Thal']
for c in Temp:
    Data[c] = Data[c].astype(int).astype(str)
del Temp, c
Target = 'Heart Disease'
Labels = ['Absent', 'Present']
Data['Heart Disease'] = (Data['Heart Disease']-1).astype(int)
#
display(Data.head(5))
display(pd.DataFrame({'Number of Instances': [Data.shape[0]], 'Number of Attributes': [Data.shape[1]]}).style.hide_index())


def Data_info(Inp, Only_NaN = False):
    Out = Inp.dtypes.to_frame(name='Data Type').sort_values(by=['Data Type'])
    Out = Out.join(Inp.isnull().sum().to_frame(name = 'Number of NaN Values'), how='outer')
    Out ['Size'] = Inp.shape[0]
    Out['Percentage'] = 100 - np.round(100*(Out['Number of NaN Values']/Inp.shape[0]),2)
    Out.index.name = 'Features'
    Out['Data Type'] = Out['Data Type'].astype(str)
    if Only_NaN:
        Out = Out.loc[Out['Number of NaN Values']>0]
    return Out

# Maps
Maps = {'Sex': {'0':'Female', '1':'Male'},
        'Chest Pain Type': {'1':'Typical Angina', '2':'Atypical Angina', '3': 'Non-Anginal Pain', '4':'Asymptomatic'},
        'Fasting Blood Sugar': {'0': 'False', '1': 'True'}, 'Exercise Induced Angina': {'0': 'No', '1': 'Yes'},
        'Slope': {'1': 'Upsloping', '2': 'Flat', '3': 'Downsloping'},
        'Thal':  {'3': 'Normal', '6': 'Fixed Defect','7': 'Reversable Defect'}}

	Age	Sex	Chest Pain Type	Resting Blood Pressure	Serum Cholestoral	Fasting Blood Sugar	Resting Electrocardiographic Results	Maximum Heart Rate Achieved	Exercise Induced Angina	Oldpeak	Slope	Number of Major Vessels	Thal	Heart Disease
0	70.0	1	4	130.0	322.0	0	2	109.0	0	2.4	2	3	3	1
1	67.0	0	3	115.0	564.0	0	2	160.0	0	1.6	2	0	7	0
2	57.0	1	2	124.0	261.0	0	0	141.0	0	0.3	1	0	7	1
3	64.0	1	4	128.0	263.0	0	0	105.0	1	0.2	2	1	7	0
4	74.0	0	2	120.0	269.0	0	2	121.0	1	0.2	1	1	3	0

Number of Instances	Number of Attributes
270	14

data_info = Data_info(Data).reset_index(drop = False)
fig = px.bar(data_info, x= 'Features', y= 'Percentage', color = 'Data Type', text = 'Data Type',
            color_discrete_sequence = ['PaleGreen', 'LightBlue', 'PeachPuff'], hover_data = data_info.columns)
fig.update_layout(plot_bgcolor= 'white', legend=dict(x=1, y=.5, traceorder="normal", bordercolor="DarkGray", borderwidth=1))
fig.update_traces(texttemplate= 6*' ' + '%{label}', textposition='inside')
fig.update_traces(marker_line_color= 'Black', marker_line_width=1., opacity=1)
fig.show()

Modeling: Tensorflow Boosted Trees Classifier with Feature Importance Analysis

Train and Test sets

# A copy of the Dataframe
df = Data.copy()
df.columns = [x.replace(' ','_') for x in df.columns] 
Temp = Target.replace(' ','_')
X = df.drop(columns = Temp)
y = df[Temp].values
del df, Temp

Test_Size = 0.3

def Sets_Plot(Data, Test_Size):
    Temp = pd.DataFrame({'Set': ['Train', 'Test'],
             'Number of Instances':[int(Data.shape[0]*(1-Test_Size)), int(Data.shape[0]*Test_Size)]})
    Temp['Percentage'] = np.round(100* Temp['Number of Instances'].values /Temp['Number of Instances'].sum(), 2)
    fig = px.bar(Temp, y= ['',''], x= 'Number of Instances', orientation='h', color = 'Set', text = 'Percentage',
                 color_discrete_sequence = ['PaleGreen', 'LightBlue'], height = 180)
    fig.update_layout(plot_bgcolor= 'white', legend_orientation='h', legend=dict(x=0, y=1.7),
                      xaxis = dict(tickmode = 'array', tickvals = [0, Data.shape[0]], ticktext = ['','']))
    fig.update_traces(marker_line_color= 'Black', marker_line_width=1.5, opacity=1)
    fig.update_traces(texttemplate='%{text:.2}%      ', textposition='inside')
    fig.update_xaxes(title_text=None, range=[0, Data.shape[0]])
    fig.update_yaxes(title_text=None)
    fig.show()
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size= Test_Size, random_state=42)
display(pd.DataFrame(data={'Set':['X_train','X_test','y_train','y_test'],
                           'Shape':[X_train.shape, X_test.shape, y_train.shape, y_test.shape]}).set_index('Set').T)
Sets_Plot(Data, Test_Size)

Set	X_train	X_test	y_train	y_test
Shape	(189, 13)	(81, 13)	(189,)	(81,)

Feature Columns

Create the feature columns, using the original numeric columns as is and one-hot-encoding categorical variables.

def Feat_Columns(Inp, Numeric = False, disp_dtype = False):
    '''
    Feature Columns function
    Input: Dataset
    Output: Tensorflow Feature Column List
    '''
    if not Numeric:
        Numeric = ['int64', 'int32', 'float64', 'float32']
    Temp = Inp.dtypes.reset_index(drop = False)
    Temp.columns = ['Features', 'Data Type']
    Temp['Data Type'] = Temp['Data Type'].astype(str)
    # Numeric_Columns
    Numeric_Columns = Temp.loc[Temp['Data Type'].isin(Numeric), 'Features'].tolist()
    # Categorical_Columns
#     Categorical_Columns = Temp.loc[(~Temp['Data Type'].isin(Numeric)), 'Features'].tolist()
    Categorical_Columns = Temp.loc[Temp['Data Type'] == 'object','Features'].tolist()
    if disp_dtype:
        display(pd.DataFrame({'Numeric Columns': [', '.join(Numeric_Columns)],
                  'Categorical Columns': [', '.join(Categorical_Columns)]}, index = ['Columns']).T.style)
    # Feature Columns
    feature_columns = []
    if len(Categorical_Columns)>0:
        for feature_name in Categorical_Columns:
            vocabulary = Inp[feature_name].unique()
            feature_columns.append(tf.feature_column.indicator_column(\
                                      tf.feature_column.categorical_column_with_vocabulary_list(feature_name, vocabulary)))
    if len(Numeric_Columns)>0:
        for feature_name in Numeric_Columns:
            feature_columns.append(tf.feature_column.numeric_column(feature_name))
    return feature_columns

Input Function

The input function specifies how data is converted to a tf.data.Dataset that feeds the input pipeline in a streaming fashion. Moreover, an input function is a function that returns a tf.data.Dataset object which outputs the following two-element tuple:

• features - A Python dictionary in which:
  • Each key is the name of a feature.
  • Each value is an array containing all of that feature's values.
• label - An array containing the values of the label for every example.

def make_input_fn(X, y, inmemory_train = False, n_epochs= None, shuffle=True, batch_size = 256):
    # Not In memory Training
    if not inmemory_train:
        def input_fn():
            dataset = tf.data.Dataset.from_tensor_slices((X.to_dict(orient='list'), y))
            if shuffle:
                dataset = dataset.shuffle(1000)
            dataset = (dataset.repeat(n_epochs).batch(batch_size))
            return dataset
    # In memory Training
    if inmemory_train:
        y = np.expand_dims(y, axis=1)
        def input_fn():
            return dict(X), y
    # End
    return input_fn

Building the input pipeline

my_feature_columns = Feat_Columns(X)
# Training and evaluation input functions.
train_input_fn = make_input_fn(X_train, y_train)
eval_input_fn = make_input_fn(X_test, y_test, shuffle=False, n_epochs=1)

Training the model

# Classifier
tf.keras.backend.clear_session()
IT = int(1e3)
params = {'n_trees': 50, 'max_depth': 3, 'n_batches_per_layer': 1, 'center_bias': True}
classifier =  tf.estimator.BoostedTreesClassifier(my_feature_columns, **params)
# Train model.
start = timer()
classifier.train(train_input_fn, max_steps = IT)
CPU_Time = timer() - start
# Evaluation.
results = classifier.evaluate(eval_input_fn)
clear_output()
results['CPU Time'] = CPU_Time
display(pd.DataFrame(results, index = ['']).round(4))

	accuracy	accuracy_baseline	auc	auc_precision_recall	average_loss	label/mean	loss	precision	prediction/mean	recall	global_step	CPU Time
	0.7778	0.6049	0.8865	0.8565	0.4267	0.3951	0.4267	0.7917	0.3231	0.5938	172	5.7731

An alternative way to train a model with boosting performance is using the train_in_memory feature. However, if there is no issue with performance or long training time is not a concern, training without this feature is recommended [5]. Furthermore, our observations have shown that using train_in_memory not always increases the performance of the training.

in_memory_params = dict(params)
in_memory_params['n_batches_per_layer'] = 1
# In-memory input_fn does not use batching.
train_input_fn = make_input_fn(X_train, y_train, inmemory_train = True)

# Classifier
tf.keras.backend.clear_session()
classifier =  tf.estimator.BoostedTreesClassifier(my_feature_columns, train_in_memory=True, **in_memory_params)
# Train model.
start = timer()
classifier.train(train_input_fn, max_steps = IT)
CPU_Time = timer() - start
# Evaluation.
results = classifier.evaluate(eval_input_fn)
clear_output()
results['CPU Time'] = CPU_Time
display(pd.DataFrame(results, index = ['']).round(4))

	accuracy	accuracy_baseline	auc	auc_precision_recall	average_loss	label/mean	loss	precision	prediction/mean	recall	global_step	CPU Time
	0.7778	0.6049	0.8791	0.8402	0.4493	0.3951	0.4493	0.7692	0.3399	0.625	152	7.6655

Feature Importance

We can investigate the feature importance of an artificial classification task. This is similar to that of scikit-learn and has been outlined in [6].

pred_dicts = list(classifier.experimental_predict_with_explanations(eval_input_fn))
clear_output()

# Create DFC Pandas dataframe.
labels = y_test
probs = pd.Series([pred['probabilities'][1] for pred in pred_dicts])
df_dfc = pd.DataFrame([pred['dfc'] for pred in pred_dicts])
display(df_dfc.describe().T.style.background_gradient(subset= ['mean'], cmap='RdYlGn')\
        .background_gradient(subset= ['std'], cmap='RdYlGn')\
        .background_gradient(subset= ['min'], cmap='hot')\
        .background_gradient(subset= ['max'], cmap='winter').set_precision(4))

	count	mean	std	min	25%	50%	75%	max
Number_of_Major_Vessels	81.0000	0.0084	0.0890	-0.1439	-0.0530	-0.0272	0.0559	0.2279
Oldpeak	81.0000	-0.0356	0.1130	-0.1624	-0.0978	-0.0811	-0.0072	0.4197
Chest_Pain_Type	81.0000	-0.0093	0.0831	-0.1366	-0.0779	-0.0483	0.0765	0.1480
Serum_Cholestoral	81.0000	-0.0176	0.0562	-0.1421	-0.0436	-0.0244	0.0029	0.1748
Slope	81.0000	-0.0000	0.0407	-0.1121	-0.0319	-0.0175	0.0304	0.0811
Thal	81.0000	-0.0300	0.0935	-0.2528	-0.0963	-0.0635	0.0551	0.2391
Resting_Blood_Pressure	81.0000	0.0120	0.0761	-0.2181	-0.0251	-0.0062	0.0295	0.3317
Maximum_Heart_Rate_Achieved	81.0000	-0.0103	0.0516	-0.2139	-0.0276	-0.0101	0.0130	0.1150
Resting_Electrocardiographic_Results	81.0000	0.0054	0.0167	-0.0276	-0.0027	0.0000	0.0095	0.0639
Sex	81.0000	-0.0050	0.0480	-0.1398	-0.0444	0.0067	0.0220	0.1114
Exercise_Induced_Angina	81.0000	-0.0198	0.0423	-0.1072	-0.0467	-0.0333	-0.0117	0.1118
Age	81.0000	-0.0240	0.0543	-0.1478	-0.0584	-0.0343	0.0016	0.1604
Fasting_Blood_Sugar	81.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000

A nice property of DFCs is that the sum of the contributions + the bias is equal to the prediction for a given example.

# Sum of DFCs + bias == probabality.
bias = pred_dicts[0]['bias']
dfc_prob = df_dfc.sum(axis=1) + bias
np.testing.assert_almost_equal(dfc_prob.values, probs.values)

Feature Importance for a patient

Plot DFCs for an individual patient which is color-coded based on the contributions' directionality and add the feature values on the figure.

def _add_feature_values(feature_values, ax, colors):
    """Display feature's values on left of plot."""
    x_coord = ax.get_xlim()[0]
    OFFSET = 0.15
    for y_coord, (feat_name, feat_val) in enumerate(feature_values.items()):
        t = plt.text(x_coord, y_coord - OFFSET, '{}'.format(feat_val), size=12)
        t.set_bbox(dict(facecolor= colors[y_coord], alpha=0.25))
    font = FontProperties()
#     font.set_weight('bold')
    t = plt.text(x_coord, y_coord + 1 - OFFSET, 'Feature\nValue', fontproperties=font, size=13)

def _yaxis_labels(ax):
    y_labels = []
    for c in [c.get_text() for c in ax.get_yticklabels()]:
        List = list(mit.locate(c, lambda x: x == " "))
        if len(List)>1:
            List = List[1::2]
            Temp1 = list(c)
            for position in List:
                Temp1[position] = '\n'
            c = "".join(Temp1)
        y_labels.append(c)
    return y_labels

def _xLims(ax):
    Temp = np.linspace(-1,1,21, endpoint=True)
    Temp = np.round(Temp,1)
    xlims = ax.get_xlim()
    for l, r in list(zip(Temp[:-1],Temp[1:])):
        if l<= xlims[0] < r:
            Left = l
        if l<= xlims[1] < r:
            Right = r
    return [Left, Right]

def Plot_Example(example, TOP_N = 10, Pos_Color = 'LimeGreen', Neg_Color = 'OrangeRed', Maps = Maps, FS = (13, 7)):
    example.index = [x.replace('_',' ') for x in example.index]
    # Sorting by absolute value
    sorted_ix = example.abs().sort_values()[-TOP_N:].index
    example = example[sorted_ix]
    
    fig, ax = plt.subplots(1, 1, figsize= FS)
    Temp = example.to_frame('Value').sort_index(ascending= False)
    _ = Temp.plot(kind='barh', color='None', edgecolor = 'Black', legend=None, alpha=1, lw=1.2, ax = ax)
    _ = Temp.loc[Temp['Value']>=0].plot(kind='barh', color= Pos_Color, edgecolor = 'white', hatch = '///',
                                 legend=None, alpha=0.75, ax = ax)
    _ = Temp.loc[Temp['Value']<0].plot(kind='barh', color= Neg_Color, edgecolor = 'white', hatch = '///',
                                 legend=None, alpha=0.75, ax = ax)
    _ = Temp.plot(kind='barh', color='None', edgecolor = 'Black', legend=None, alpha=1, lw=1.2, ax = ax)
    del Temp
    _ = ax.grid(False, axis='y')
    # Y axis Labels

    _ = ax.set_yticklabels(_yaxis_labels(ax), size=12)
    # x axis Limits
    _ = ax.set_xlim(_xLims(ax))
    
    # Add feature values.
    Temp = X_test.copy()
    Temp.columns = [x.replace('_',' ') for x in Temp.columns]
    for c in Maps.keys():
        Temp[c] = Temp[c].map(Maps[c])
  
    colors = example.map(lambda x: Pos_Color if x >= 0 else Neg_Color).tolist()
    _add_feature_values(Temp.iloc[ID][sorted_ix], ax, colors)
    return ax

# Plot results.
# ID = np.random.choice(len(y_test), 1)[0]
ID = 61
Tops = X_train.shape[1]
ax = Plot_Example(df_dfc.iloc[ID], TOP_N = Tops, FS = (13, 9))
_ = ax.set_title('Feature contributions for example patient {} from the Test set\n Pred: {:1.2f}; Label: {}'
                 .format(ID, probs[ID], labels[ID]))
_ = ax.set_xlabel('Contribution to Predicted Probability', size=14)

Global feature importances

Gain-based feature importances

Gain-based feature importances are built into the TensorFlow Boosted Trees estimators using classifier.experimental_feature_importances.

importances = classifier.experimental_feature_importances(normalize=True)
df_imp = pd.Series(importances)
Temp = df_imp.iloc[0:Tops][::-1].reset_index()
Temp.columns = ['Features','Importance']
Temp['Features'] = Temp['Features'].map(lambda x: x.replace('_',' '))

importances = classifier.experimental_feature_importances(normalize=True)

def Plot_FeatImportance(pds, TOP_N = 10, FS = (13, 6)):
    Temp = pds.iloc[0:TOP_N][::-1].reset_index()
    Temp.columns = ['Features','Importance']
    Temp = Temp.sort_values(by=['Importance'])
    Temp['Features'] = Temp['Features'].map(lambda x: x.replace('_',' '))
    
    fig, ax = plt.subplots(1, 1, figsize = FS)
    CP = sns.color_palette("RdYlGn", TOP_N)
    _ = sns.barplot(ax = ax, x='Importance', y= 'Features', data= Temp, palette=CP, hatch = '//')
    _ = sns.barplot(ax = ax, x='Importance', y= 'Features', data= Temp, facecolor = 'None', edgecolor = 'Indigo')
    _ = ax.grid(False, axis='y')
    # Y axis Labels
    _ = ax.set_yticklabels(_yaxis_labels(ax), size=12)
    # x axis Limits
    _ = ax.set_xlim(_xLims(ax))
    return ax
    
ax = Plot_FeatImportance(pd.Series(importances), TOP_N = Tops, FS = (13, 7.5))
_ = ax.set_xlim(right = .16)

Average absolute DFCs

ax = Plot_FeatImportance(df_dfc.abs().mean(), TOP_N = Tops, FS = (13, 7.5))
_ = ax.set_xlim(right = .1)

Permutation feature importance

def permutation_importances(est, X_eval, y_test, metric, features):
    """Column by column, shuffle values and observe effect on eval set.

    source: http://explained.ai/rf-importance/index.html
    A similar approach can be done during training. See "Drop-column importance"
    in the above article."""
    baseline = metric(est, X_eval, y_test)
    imp = []
    for col in features:
        save = X_eval[col].copy()
        X_eval[col] = np.random.permutation(X_eval[col])
        m = metric(est, X_eval, y_test)
        X_eval[col] = save
        imp.append(baseline - m)
    return np.array(imp)

def accuracy_metric(est, X, y):
    """TensorFlow estimator accuracy."""
    eval_input_fn = make_input_fn(X,
                                  y=y,
                                  shuffle=False,
                                  n_epochs=1)
    return est.evaluate(input_fn=eval_input_fn)['accuracy']
features = X_train.columns.tolist()
importances = permutation_importances(classifier, X_test, y_test, accuracy_metric,
                                      features)
df_imp = pd.Series(importances, index=features)
clear_output()

_ = Plot_FeatImportance(df_imp)

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References

1. Detrano, R., Janosi, A., Steinbrunn, W., Pfisterer, M., Schmid, J.J., Sandhu, S., Guppy, K.H., Lee, S. and Froelicher, V., 1989. International application of a new probability algorithm for the diagnosis of coronary artery disease. The American journal of cardiology, 64(5), pp.304-310.

2. Aha, D. and Kibler, D., 1988. Instance-based prediction of heart-disease presence with the Cleveland database. University of California, 3(1), pp.3-2.

3. Gennari, J.H., Langley, P. and Fisher, D., 1989. Models of incremental concept formation. Artificial intelligence, 40(1-3), pp.11-61.

4. Regression analysis. Wikipedia. Last edited on 17 April 2020, at 13:31 (UTC). https://en.wikipedia.org/wiki/Regression_analysis
5. Tensorflow tutorials, https://www.tensorflow.org/tutorials
6. TensorFlow Boosted Trees Classifier, https://www.tensorflow.org/api_docs/python/tf/estimator/BoostedTreesClassifier?version=nightly
7. Lasso (statistics), https://en.wikipedia.org/wiki/Lasso_(statistics).
8. Tikhonov regularizationm https://en.wikipedia.org/wiki/Tikhonov_regularization.
9. Palczewska A., Palczewski J., Marchese Robinson R., Neagu D. (2014) Interpreting Random Forest Classification Models Using a Feature Contribution Method. In: Bouabana-Tebibel T., Rubin S. (eds) Integration of Reusable Systems. Advances in Intelligent Systems and Computing, vol 263. Springer, Cham
10. James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, pp. 3-7). New York: springer.
11. Jordi Warmenhoven, ISLR-python
12. James, G., Witten, D., Hastie, T., & Tibshirani, R. (2017). ISLR: Data for an Introduction to Statistical Learning with Applications in R

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